Nope, it behaves fine. The owner of the network is serving under age kids. Push too far and its white lists only and block all other IP and I'm sure we'll get deep packet inspection forced on us. Some folks have serious problems with Google Images Search, but you can actually deal with that.
I would also say anyone hard coding DNS into a device is just absolutely unprofessional. Its basically a red flag that any filtering the owner of the network doesn't matter to them.
I'm generally inclined to think an "always use this manually-configured DNS" option is desirable in that situation. Of course, many devices may have a financial incentive (ads) to actively resist the network owner's attempts at filtering.
Filtering is inherently adversarial, and I expect a reasonably sophisticated user on your network could find a way to access some proscribed content. I also expect the users of concern on your network are under five years old and that most of them lack advanced knowledge of networking. Is there an established standard for what qualifies as a reliable-enough filter?
Designing a device to connect to something over the internet even if the network it's connected to behaves strangely isn't random or stupid; it's just in conflict with your goals. Incidentally, last time I ran into a network with legally mandated filtering, I checked whether a google image search for "tits" worked. It did.